TSTP Solution File: GRP025-1 by SATCoP---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SATCoP---0.1
% Problem : GRP025-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : satcop --statistics %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:31:37 EDT 2022
% Result : Unsatisfiable 38.79s 5.32s
% Output : Proof 38.79s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,plain,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product_holds_in_group2)]) ).
cnf(g1,plain,
sPE(g2,g2),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g2,plain,
product(g2,g2,identity_for(g2),g2),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',right_identity)]) ).
cnf(g3,plain,
product(g2,an_isomorphism(d1),identity_for(g2),an_isomorphism(d1)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',right_identity)]) ).
cnf(g4,plain,
sPE(an_isomorphism(d1),an_isomorphism(d1)),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g5,plain,
product(g2,identity_for(g2),an_isomorphism(d1),an_isomorphism(d1)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',left_identity)]) ).
cnf(g6,plain,
( ~ group_member(an_isomorphism(d1),g2)
| ~ group_member(an_isomorphism(d2),g2)
| product(g2,an_isomorphism(d1),an_isomorphism(d2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function1_1)]) ).
cnf(g7,plain,
sPE(an_isomorphism(d2),an_isomorphism(d2)),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g8,plain,
product(g2,inverse(g2,an_isomorphism(d2)),an_isomorphism(d2),identity_for(g2)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',left_inverse)]) ).
cnf(g9,plain,
( ~ group_member(an_isomorphism(d1),g2)
| ~ group_member(identity_for(g2),g2)
| product(g2,an_isomorphism(d1),identity_for(g2),multiply(g2,an_isomorphism(d1),identity_for(g2))) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function1_1)]) ).
cnf(g10,plain,
sPE(an_isomorphism(d3),an_isomorphism(d3)),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g11,plain,
product(g2,identity_for(g2),g2,g2),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',left_identity)]) ).
cnf(g12,plain,
product(g2,an_isomorphism(d3),identity_for(g2),an_isomorphism(d3)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',right_identity)]) ).
cnf(g13,plain,
( ~ product(g2,an_isomorphism(d3),inverse(g2,an_isomorphism(d2)),an_isomorphism(d1))
| ~ product(g2,an_isomorphism(d3),identity_for(g2),an_isomorphism(d3))
| ~ product(g2,inverse(g2,an_isomorphism(d2)),an_isomorphism(d2),identity_for(g2))
| product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity2)]) ).
cnf(g14,plain,
product(g1,d1,d2,d3),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_times_d2_is_d3)]) ).
cnf(g15,plain,
( ~ group_member(d2,g1)
| sPE(d2,a)
| sPE(d2,b) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_and_b_only_members_of_group1)]) ).
cnf(g16,plain,
( ~ group_member(d3,g1)
| sPE(d3,a)
| sPE(d3,b) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_and_b_only_members_of_group1)]) ).
cnf(g17,plain,
sPE(d3,d3),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g18,plain,
product(g2,d,c,d),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_c_is_d)]) ).
cnf(g19,plain,
( ~ sPE(g2,g2)
| sPE(identity_for(g2),identity_for(g2)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g20,plain,
product(g2,d,d,c),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_d_is_c)]) ).
cnf(g21,plain,
product(g2,identity_for(g2),identity_for(g2),identity_for(g2)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',left_identity)]) ).
cnf(g22,plain,
product(g2,g2,inverse(g2,g2),identity_for(g2)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',right_inverse)]) ).
cnf(g23,plain,
( ~ sPE(an_isomorphism(d1),d)
| sPE(d,an_isomorphism(d1)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g24,plain,
product(g1,b,a,b),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_is_b)]) ).
cnf(g25,plain,
product(g2,c,d,d),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_d_is_d)]) ).
cnf(g26,plain,
group_member(identity_for(g2),g2),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',identity_in_group)]) ).
cnf(g27,plain,
product(g2,c,c,c),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_c_is_c)]) ).
cnf(g28,plain,
( ~ group_member(identity_for(g2),g2)
| ~ group_member(an_isomorphism(d1),g2)
| product(g2,identity_for(g2),an_isomorphism(d1),multiply(g2,identity_for(g2),an_isomorphism(d1))) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function1_1)]) ).
cnf(g29,plain,
( ~ product(g2,an_isomorphism(d1),identity_for(g2),an_isomorphism(d1))
| ~ product(g2,an_isomorphism(d1),identity_for(g2),multiply(g2,an_isomorphism(d1),identity_for(g2)))
| sPE(multiply(g2,an_isomorphism(d1),identity_for(g2)),an_isomorphism(d1)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g30,plain,
product(g2,inverse(g2,g2),g2,identity_for(g2)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',left_inverse)]) ).
cnf(g31,plain,
product(g2,an_isomorphism(d2),inverse(g2,an_isomorphism(d2)),identity_for(g2)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',right_inverse)]) ).
cnf(g32,plain,
sPE(inverse(g2,an_isomorphism(d2)),inverse(g2,an_isomorphism(d2))),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g33,plain,
product(g1,a,b,b),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_b)]) ).
cnf(g34,plain,
( ~ group_member(c,g2)
| ~ group_member(d,g2)
| product(g2,c,d,multiply(g2,c,d)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function1_1)]) ).
cnf(g35,plain,
product(g1,a,a,a),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_a_is_a)]) ).
cnf(g36,plain,
product(g2,identity_for(g2),c,c),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',left_identity)]) ).
cnf(g37,plain,
product(g2,inverse(g2,c),c,identity_for(g2)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',left_inverse)]) ).
cnf(g38,plain,
( ~ sPE(d2,d3)
| sPE(an_isomorphism(d2),an_isomorphism(d3)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g39,plain,
product(g2,identity_for(g2),d,d),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',left_identity)]) ).
cnf(g40,plain,
( ~ product(g2,identity_for(g2),d,d)
| ~ product(g2,identity_for(g2),d,an_isomorphism(d2))
| ~ product(g2,d,c,d)
| product(g2,d,c,an_isomorphism(d2)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity2)]) ).
cnf(g41,plain,
product(g2,c,identity_for(g2),c),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',right_identity)]) ).
cnf(g42,plain,
product(g1,b,b,a),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_b_is_a)]) ).
cnf(g43,plain,
group_member(d2,g1),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_member_of_group1)]) ).
cnf(g44,plain,
sPE(an_isomorphism(a),c),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_maps_to_c)]) ).
cnf(g45,plain,
group_member(c,g2),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_member_of_group2)]) ).
cnf(g46,plain,
group_member(d3,g1),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_member_of_group1)]) ).
cnf(g47,plain,
( ~ product(g2,identity_for(g2),an_isomorphism(d1),an_isomorphism(d1))
| ~ product(g2,identity_for(g2),an_isomorphism(d1),multiply(g2,identity_for(g2),an_isomorphism(d1)))
| sPE(multiply(g2,identity_for(g2),an_isomorphism(d1)),an_isomorphism(d1)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g48,plain,
group_member(d,g2),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_member_of_group2)]) ).
cnf(g49,plain,
product(g2,d,identity_for(g2),d),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',right_identity)]) ).
cnf(g50,plain,
sPE(g1,g1),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g51,plain,
( ~ group_member(d1,g1)
| sPE(d1,a)
| sPE(d1,b) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_and_b_only_members_of_group1)]) ).
cnf(g52,plain,
( ~ product(g2,d,c,an_isomorphism(d2))
| ~ product(g2,d,c,d)
| sPE(d,an_isomorphism(d2)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g53,plain,
( ~ sPE(d1,b)
| sPE(an_isomorphism(d1),an_isomorphism(b)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g54,plain,
( ~ sPE(an_isomorphism(d1),an_isomorphism(a))
| sPE(an_isomorphism(a),an_isomorphism(d1)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g55,plain,
( ~ sPE(d1,a)
| sPE(an_isomorphism(d1),an_isomorphism(a)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g56,plain,
( ~ sPE(d3,b)
| sPE(an_isomorphism(d3),an_isomorphism(b)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g57,plain,
( ~ sPE(d3,a)
| sPE(an_isomorphism(d3),an_isomorphism(a)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g58,plain,
( ~ sPE(an_isomorphism(a),c)
| sPE(c,an_isomorphism(a)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g59,plain,
sPE(an_isomorphism(a),an_isomorphism(a)),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g60,plain,
( ~ sPE(a,d3)
| sPE(an_isomorphism(a),an_isomorphism(d3)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g61,plain,
( ~ sPE(d3,a)
| sPE(a,d3) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g62,plain,
( ~ sPE(an_isomorphism(d2),an_isomorphism(a))
| sPE(an_isomorphism(a),an_isomorphism(d2)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g63,plain,
( ~ sPE(d2,a)
| sPE(an_isomorphism(d2),an_isomorphism(a)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g64,plain,
( ~ sPE(an_isomorphism(d2),an_isomorphism(b))
| sPE(an_isomorphism(b),an_isomorphism(d2)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g65,plain,
( ~ sPE(d2,b)
| sPE(an_isomorphism(d2),an_isomorphism(b)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g66,plain,
( ~ sPE(g2,g2)
| ~ sPE(an_isomorphism(d1),an_isomorphism(d1))
| ~ sPE(an_isomorphism(b),an_isomorphism(d2))
| ~ sPE(an_isomorphism(a),an_isomorphism(d3))
| ~ product(g2,an_isomorphism(d1),an_isomorphism(b),an_isomorphism(a))
| product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g67,plain,
product(g2,identity_for(g2),an_isomorphism(a),an_isomorphism(a)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',left_identity)]) ).
cnf(g68,plain,
( ~ sPE(b,a)
| sPE(an_isomorphism(b),an_isomorphism(a)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g69,plain,
product(g2,an_isomorphism(b),identity_for(g2),an_isomorphism(b)),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',right_identity)]) ).
cnf(g70,plain,
( ~ sPE(an_isomorphism(b),d)
| sPE(d,an_isomorphism(b)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g71,plain,
sPE(an_isomorphism(b),d),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_maps_to_d)]) ).
cnf(g72,plain,
( ~ sPE(b,d3)
| sPE(an_isomorphism(b),an_isomorphism(d3)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g73,plain,
( ~ sPE(d3,b)
| sPE(b,d3) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g74,plain,
product(g2,multiply(g2,an_isomorphism(d1),identity_for(g2)),identity_for(g2),multiply(g2,an_isomorphism(d1),identity_for(g2))),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',right_identity)]) ).
cnf(g75,plain,
( ~ product(g2,identity_for(g2),c,c)
| ~ product(g2,identity_for(g2),c,identity_for(g2))
| ~ product(g2,c,c,c)
| product(g2,c,c,identity_for(g2)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity2)]) ).
cnf(g76,plain,
( ~ sPE(an_isomorphism(b),c)
| sPE(c,an_isomorphism(b)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g77,plain,
( ~ sPE(c,d)
| sPE(d,c) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g78,plain,
( ~ sPE(c,identity_for(g2))
| sPE(identity_for(g2),c) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g79,plain,
( ~ product(g2,inverse(g2,g2),g2,identity_for(g2))
| ~ product(g2,g2,an_isomorphism(a),g2)
| ~ product(g2,identity_for(g2),an_isomorphism(a),an_isomorphism(a))
| product(g2,inverse(g2,g2),g2,an_isomorphism(a)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity1)]) ).
cnf(g80,plain,
( ~ sPE(g2,g2)
| ~ sPE(g2,g2)
| ~ sPE(identity_for(g2),c)
| ~ sPE(g2,g2)
| ~ product(g2,g2,identity_for(g2),g2)
| product(g2,g2,c,g2) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g81,plain,
( ~ product(g2,an_isomorphism(d1),identity_for(g2),c)
| ~ product(g2,identity_for(g2),g2,g2)
| ~ product(g2,c,g2,g2)
| product(g2,an_isomorphism(d1),g2,g2) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity1)]) ).
cnf(g82,plain,
( ~ product(g2,c,d,multiply(g2,c,d))
| ~ product(g2,c,c,c)
| ~ product(g2,d,d,c)
| product(g2,multiply(g2,c,d),d,c) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity2)]) ).
cnf(g83,plain,
( ~ sPE(g2,g2)
| ~ sPE(multiply(g2,c,d),an_isomorphism(d1))
| ~ sPE(d,an_isomorphism(b))
| ~ sPE(c,an_isomorphism(a))
| ~ product(g2,multiply(g2,c,d),d,c)
| product(g2,an_isomorphism(d1),an_isomorphism(b),an_isomorphism(a)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g84,plain,
( ~ sPE(multiply(g2,c,d),d)
| ~ sPE(d,an_isomorphism(d1))
| sPE(multiply(g2,c,d),an_isomorphism(d1)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g85,plain,
group_member(d1,g1),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_member_of_group1)]) ).
cnf(g86,plain,
( ~ sPE(g2,g2)
| ~ sPE(identity_for(g2),c)
| ~ sPE(g2,g2)
| ~ sPE(g2,g2)
| ~ product(g2,identity_for(g2),g2,g2)
| product(g2,c,g2,g2) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g87,plain,
( ~ sPE(c,an_isomorphism(d2))
| ~ sPE(g2,g2)
| ~ group_member(c,g2)
| group_member(an_isomorphism(d2),g2) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g88,plain,
( ~ sPE(b,d3)
| sPE(d3,b) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g89,plain,
( ~ sPE(g2,g2)
| ~ sPE(an_isomorphism(b),d)
| ~ sPE(identity_for(g2),identity_for(g2))
| ~ sPE(an_isomorphism(b),an_isomorphism(d2))
| ~ product(g2,an_isomorphism(b),identity_for(g2),an_isomorphism(b))
| product(g2,d,identity_for(g2),an_isomorphism(d2)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g90,plain,
( ~ sPE(d,an_isomorphism(d1))
| ~ sPE(g2,g2)
| ~ group_member(d,g2)
| group_member(an_isomorphism(d1),g2) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g91,plain,
( ~ sPE(a,b)
| sPE(b,a) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g92,plain,
( ~ sPE(c,an_isomorphism(d1))
| ~ sPE(g2,g2)
| ~ group_member(c,g2)
| group_member(an_isomorphism(d1),g2) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g93,plain,
( ~ sPE(c,an_isomorphism(a))
| ~ sPE(an_isomorphism(a),an_isomorphism(d2))
| sPE(c,an_isomorphism(d2)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g94,plain,
( ~ product(g2,identity_for(g2),d,d)
| ~ product(g2,d,identity_for(g2),d)
| ~ product(g2,d,identity_for(g2),an_isomorphism(d2))
| product(g2,identity_for(g2),d,an_isomorphism(d2)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity1)]) ).
cnf(g95,plain,
( ~ sPE(an_isomorphism(d1),an_isomorphism(b))
| ~ sPE(an_isomorphism(b),d)
| sPE(an_isomorphism(d1),d) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g96,plain,
( ~ product(g2,inverse(g2,c),c,identity_for(g2))
| ~ product(g2,inverse(g2,c),c,identity_for(g2))
| ~ product(g2,c,c,c)
| product(g2,identity_for(g2),c,identity_for(g2)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity2)]) ).
cnf(g97,plain,
( ~ sPE(d,an_isomorphism(d2))
| ~ sPE(g2,g2)
| ~ group_member(d,g2)
| group_member(an_isomorphism(d2),g2) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g98,plain,
( ~ product(g1,b,a,d3)
| ~ product(g1,b,a,b)
| sPE(b,d3) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g99,plain,
( ~ sPE(c,an_isomorphism(a))
| ~ sPE(an_isomorphism(a),an_isomorphism(d1))
| sPE(c,an_isomorphism(d1)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g100,plain,
( ~ sPE(g2,g2)
| ~ sPE(an_isomorphism(d1),d)
| ~ sPE(g2,g2)
| ~ sPE(g2,g2)
| ~ product(g2,an_isomorphism(d1),g2,g2)
| product(g2,d,g2,g2) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g101,plain,
( ~ group_member(multiply(g2,an_isomorphism(d1),identity_for(g2)),g2)
| sPE(multiply(g2,an_isomorphism(d1),identity_for(g2)),c)
| sPE(multiply(g2,an_isomorphism(d1),identity_for(g2)),d) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_and_d_only_members_of_group2)]) ).
cnf(g102,plain,
( ~ sPE(g2,g2)
| ~ sPE(an_isomorphism(d1),an_isomorphism(d1))
| ~ sPE(identity_for(g2),identity_for(g2))
| sPE(multiply(g2,an_isomorphism(d1),identity_for(g2)),multiply(g2,an_isomorphism(d1),identity_for(g2))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g103,plain,
( ~ group_member(an_isomorphism(d1),g2)
| ~ group_member(identity_for(g2),g2)
| group_member(multiply(g2,an_isomorphism(d1),identity_for(g2)),g2) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function1_2)]) ).
cnf(g104,plain,
product(g2,identity_for(g2),multiply(g2,identity_for(g2),an_isomorphism(d1)),multiply(g2,identity_for(g2),an_isomorphism(d1))),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',left_identity)]) ).
cnf(g105,plain,
( ~ product(g1,a,b,b)
| ~ product(g1,a,b,a)
| sPE(a,b) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g106,plain,
( ~ sPE(d,c)
| sPE(c,d) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g107,plain,
( ~ sPE(an_isomorphism(d3),an_isomorphism(b))
| ~ sPE(an_isomorphism(b),d)
| sPE(an_isomorphism(d3),d) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g108,plain,
( ~ group_member(an_isomorphism(d1),g2)
| ~ group_member(an_isomorphism(d2),g2)
| group_member(multiply(g2,an_isomorphism(d1),an_isomorphism(d2)),g2) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function1_2)]) ).
cnf(g109,plain,
( ~ sPE(g2,g2)
| ~ sPE(identity_for(g2),c)
| ~ sPE(an_isomorphism(a),c)
| ~ sPE(an_isomorphism(a),an_isomorphism(a))
| ~ product(g2,identity_for(g2),an_isomorphism(a),an_isomorphism(a))
| product(g2,c,c,an_isomorphism(a)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g110,plain,
( ~ sPE(c,an_isomorphism(b))
| ~ sPE(an_isomorphism(b),d)
| sPE(c,d) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g111,plain,
( ~ product(g2,c,c,identity_for(g2))
| ~ product(g2,c,c,c)
| sPE(c,identity_for(g2)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g112,plain,
( ~ sPE(an_isomorphism(d3),an_isomorphism(a))
| ~ sPE(an_isomorphism(a),c)
| sPE(an_isomorphism(d3),c) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g113,plain,
( ~ group_member(identity_for(g2),g2)
| ~ group_member(multiply(g2,an_isomorphism(d1),an_isomorphism(d2)),g2)
| product(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function1_1)]) ).
cnf(g114,plain,
( ~ sPE(d2,b)
| ~ sPE(b,d3)
| sPE(d2,d3) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g115,plain,
( ~ sPE(g2,g2)
| ~ sPE(multiply(g2,an_isomorphism(d1),identity_for(g2)),multiply(g2,an_isomorphism(d1),identity_for(g2)))
| ~ sPE(identity_for(g2),identity_for(g2))
| ~ sPE(multiply(g2,an_isomorphism(d1),identity_for(g2)),d)
| ~ product(g2,multiply(g2,an_isomorphism(d1),identity_for(g2)),identity_for(g2),multiply(g2,an_isomorphism(d1),identity_for(g2)))
| product(g2,multiply(g2,an_isomorphism(d1),identity_for(g2)),identity_for(g2),d) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g116,plain,
( ~ sPE(an_isomorphism(d3),d)
| ~ sPE(d,c)
| sPE(an_isomorphism(d3),c) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g117,plain,
( ~ product(g2,d,g2,g2)
| ~ product(g2,g2,inverse(g2,g2),identity_for(g2))
| ~ product(g2,g2,inverse(g2,g2),identity_for(g2))
| product(g2,d,identity_for(g2),identity_for(g2)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity1)]) ).
cnf(g118,plain,
( ~ product(g2,c,identity_for(g2),c)
| ~ product(g2,c,identity_for(g2),d)
| sPE(d,c) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g119,plain,
( ~ product(g2,g2,c,g2)
| ~ product(g2,c,c,an_isomorphism(a))
| ~ product(g2,g2,c,g2)
| product(g2,g2,an_isomorphism(a),g2) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity1)]) ).
cnf(g120,plain,
( ~ sPE(an_isomorphism(d3),c)
| ~ sPE(c,d)
| sPE(an_isomorphism(d3),d) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g121,plain,
( ~ product(g2,inverse(g2,g2),g2,identity_for(g2))
| ~ product(g2,inverse(g2,g2),g2,an_isomorphism(a))
| ~ product(g2,g2,identity_for(g2),g2)
| product(g2,identity_for(g2),identity_for(g2),an_isomorphism(a)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity2)]) ).
cnf(g122,plain,
( ~ sPE(an_isomorphism(b),an_isomorphism(a))
| ~ sPE(an_isomorphism(a),c)
| sPE(an_isomorphism(b),c) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g123,plain,
( ~ sPE(g2,g2)
| ~ sPE(an_isomorphism(d1),an_isomorphism(d1))
| ~ sPE(identity_for(g2),identity_for(g2))
| ~ sPE(multiply(g2,an_isomorphism(d1),identity_for(g2)),c)
| ~ product(g2,an_isomorphism(d1),identity_for(g2),multiply(g2,an_isomorphism(d1),identity_for(g2)))
| product(g2,an_isomorphism(d1),identity_for(g2),c) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g124,plain,
( ~ product(g2,identity_for(g2),identity_for(g2),an_isomorphism(a))
| ~ product(g2,identity_for(g2),identity_for(g2),identity_for(g2))
| sPE(identity_for(g2),an_isomorphism(a)) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g125,plain,
( ~ group_member(identity_for(g2),g2)
| ~ group_member(multiply(g2,an_isomorphism(d1),an_isomorphism(d2)),g2)
| group_member(multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))),g2) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function1_2)]) ).
cnf(g126,plain,
( ~ product(g2,c,d,d)
| ~ product(g2,c,d,multiply(g2,c,d))
| sPE(multiply(g2,c,d),d) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g127,plain,
( ~ sPE(g1,g1)
| ~ sPE(d1,a)
| ~ sPE(d2,b)
| ~ sPE(d3,a)
| ~ product(g1,d1,d2,d3)
| product(g1,a,b,a) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g128,plain,
( ~ sPE(g2,g2)
| ~ sPE(an_isomorphism(d3),an_isomorphism(d3))
| ~ sPE(inverse(g2,an_isomorphism(d2)),inverse(g2,an_isomorphism(d2)))
| ~ sPE(c,an_isomorphism(d1))
| ~ product(g2,an_isomorphism(d3),inverse(g2,an_isomorphism(d2)),c)
| product(g2,an_isomorphism(d3),inverse(g2,an_isomorphism(d2)),an_isomorphism(d1)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g129,plain,
( ~ product(g2,d,d,c)
| ~ product(g2,d,identity_for(g2),d)
| ~ product(g2,d,identity_for(g2),identity_for(g2))
| product(g2,c,identity_for(g2),d) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity2)]) ).
cnf(g130,plain,
( ~ sPE(d2,a)
| ~ sPE(a,d3)
| sPE(d2,d3) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g131,plain,
( ~ product(g1,a,a,a)
| ~ product(g1,a,a,b)
| sPE(b,a) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g132,plain,
( ~ product(g2,identity_for(g2),an_isomorphism(d1),multiply(g2,identity_for(g2),an_isomorphism(d1)))
| ~ product(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))))
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))
| product(g2,multiply(g2,identity_for(g2),an_isomorphism(d1)),an_isomorphism(d2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity2)]) ).
cnf(g133,plain,
( ~ group_member(identity_for(g2),g2)
| ~ group_member(multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))),g2)
| product(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))),multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))))) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function1_1)]) ).
cnf(g134,plain,
( ~ group_member(multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))),g2)
| sPE(multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))),c)
| sPE(multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))),d) ),
inference(ground_cnf,[],[file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_and_d_only_members_of_group2)]) ).
cnf(g135,plain,
( ~ sPE(g2,g2)
| ~ sPE(multiply(g2,identity_for(g2),an_isomorphism(d1)),an_isomorphism(d1))
| ~ sPE(an_isomorphism(d2),an_isomorphism(d2))
| ~ sPE(multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))),an_isomorphism(d3))
| ~ product(g2,multiply(g2,identity_for(g2),an_isomorphism(d1)),an_isomorphism(d2),multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))))
| product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g136,plain,
( ~ product(g2,identity_for(g2),multiply(g2,identity_for(g2),an_isomorphism(d1)),multiply(g2,identity_for(g2),an_isomorphism(d1)))
| ~ product(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))),multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))))
| ~ product(g2,multiply(g2,identity_for(g2),an_isomorphism(d1)),an_isomorphism(d2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))))
| product(g2,multiply(g2,identity_for(g2),an_isomorphism(d1)),an_isomorphism(d2),multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))))) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',associativity2)]) ).
cnf(g137,plain,
( ~ sPE(multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))),d)
| sPE(d,multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g138,plain,
( ~ sPE(an_isomorphism(d3),multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))))
| sPE(multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))),an_isomorphism(d3)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g139,plain,
( ~ sPE(an_isomorphism(d3),c)
| ~ sPE(c,multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))))
| sPE(an_isomorphism(d3),multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g140,plain,
( ~ sPE(an_isomorphism(d3),d)
| ~ sPE(d,multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))))
| sPE(an_isomorphism(d3),multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g141,plain,
( ~ group_member(identity_for(g2),g2)
| ~ group_member(multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))),g2)
| group_member(multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))),g2) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function1_2)]) ).
cnf(g142,plain,
( ~ sPE(multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2)))),c)
| sPE(c,multiply(g2,identity_for(g2),multiply(g2,identity_for(g2),multiply(g2,an_isomorphism(d1),an_isomorphism(d2))))) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g143,plain,
( ~ sPE(g2,g2)
| ~ sPE(an_isomorphism(d2),an_isomorphism(d3))
| ~ sPE(inverse(g2,an_isomorphism(d2)),inverse(g2,an_isomorphism(d2)))
| ~ sPE(identity_for(g2),c)
| ~ product(g2,an_isomorphism(d2),inverse(g2,an_isomorphism(d2)),identity_for(g2))
| product(g2,an_isomorphism(d3),inverse(g2,an_isomorphism(d2)),c) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g144,plain,
( ~ product(g1,b,b,a)
| ~ product(g1,b,b,b)
| sPE(b,a) ),
inference(ground_cnf,[],[file('Axioms/GRP006-0.ax',total_function2)]) ).
cnf(g145,plain,
( ~ sPE(g2,g2)
| ~ sPE(multiply(g2,an_isomorphism(d1),identity_for(g2)),an_isomorphism(d1))
| ~ sPE(an_isomorphism(a),an_isomorphism(d2))
| ~ sPE(an_isomorphism(b),an_isomorphism(d3))
| ~ product(g2,multiply(g2,an_isomorphism(d1),identity_for(g2)),an_isomorphism(a),an_isomorphism(b))
| product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g146,plain,
( ~ sPE(g2,g2)
| ~ sPE(multiply(g2,an_isomorphism(d1),identity_for(g2)),multiply(g2,an_isomorphism(d1),identity_for(g2)))
| ~ sPE(identity_for(g2),an_isomorphism(a))
| ~ sPE(d,an_isomorphism(b))
| ~ product(g2,multiply(g2,an_isomorphism(d1),identity_for(g2)),identity_for(g2),d)
| product(g2,multiply(g2,an_isomorphism(d1),identity_for(g2)),an_isomorphism(a),an_isomorphism(b)) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g147,plain,
( ~ sPE(g1,g1)
| ~ sPE(d1,a)
| ~ sPE(d2,a)
| ~ sPE(d3,b)
| ~ product(g1,d1,d2,d3)
| product(g1,a,a,b) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g148,plain,
( ~ sPE(g1,g1)
| ~ sPE(d1,b)
| ~ sPE(d2,a)
| ~ sPE(d3,d3)
| ~ product(g1,d1,d2,d3)
| product(g1,b,a,d3) ),
inference(ground_cnf,[],[theory(equality)]) ).
cnf(g149,plain,
( ~ sPE(g1,g1)
| ~ sPE(d1,b)
| ~ sPE(d2,b)
| ~ sPE(d3,b)
| ~ product(g1,d1,d2,d3)
| product(g1,b,b,b) ),
inference(ground_cnf,[],[theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP025-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : satcop --statistics %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 05:44:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 38.79/5.32 % symbols: 17
% 38.79/5.32 % clauses: 41
% 38.79/5.32 % start clauses: 1
% 38.79/5.32 % iterative deepening steps: 5148
% 38.79/5.32 % maximum path limit: 6
% 38.79/5.32 % literal attempts: 1674220
% 38.79/5.32 % depth failures: 1003712
% 38.79/5.32 % regularity failures: 21844
% 38.79/5.32 % tautology failures: 100894
% 38.79/5.32 % reductions: 2151
% 38.79/5.32 % extensions: 1667766
% 38.79/5.32 % SAT variables: 214874
% 38.79/5.32 % SAT clauses: 627667
% 38.79/5.32 % WalkSAT solutions: 626797
% 38.79/5.32 % CDCL solutions: 863
% 38.79/5.32 % SZS status Unsatisfiable for theBenchmark
% 38.79/5.32 % SZS output start ListOfCNF for theBenchmark
% See solution above
%------------------------------------------------------------------------------