TSTP Solution File: SYN195-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN195-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n006.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 : 300s
% DateTime : Fri Sep 1 03:33:32 EDT 2023
% Result : Unsatisfiable 32.52s 4.53s
% Output : Proof 32.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN195-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 19:20:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 32.52/4.53 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 32.52/4.53
% 32.52/4.53 % SZS status Unsatisfiable
% 32.52/4.53
% 32.52/4.54 % SZS output start Proof
% 32.52/4.54 Take the following subset of the input axioms:
% 32.52/4.54 fof(axiom_17, axiom, ![X]: q0(X, d)).
% 32.52/4.54 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 32.52/4.54 fof(axiom_32, axiom, k0(b)).
% 32.52/4.54 fof(axiom_34, axiom, n0(c, d)).
% 32.52/4.54 fof(prove_this, negated_conjecture, ~r5(d, d)).
% 32.52/4.54 fof(rule_002, axiom, ![G, H]: (l1(G, G) | ~n0(H, G))).
% 32.52/4.54 fof(rule_107, axiom, ![A2]: (q1(e, A2, A2) | (~m0(A2, d, A2) | ~m0(e, d, A2)))).
% 32.52/4.54 fof(rule_122, axiom, ![H2, G2]: (q1(G2, G2, G2) | ~m0(G2, H2, G2))).
% 32.52/4.54 fof(rule_129, axiom, ![J, A]: (k2(J, J) | ~q1(A, J, J))).
% 32.52/4.54 fof(rule_154, axiom, ![A2_2]: (p2(A2_2, A2_2, A2_2) | ~q1(A2_2, A2_2, A2_2))).
% 32.52/4.54 fof(rule_240, axiom, ![D, E, F]: (n3(D) | ~p2(E, F, D))).
% 32.52/4.54 fof(rule_252, axiom, ![I, J2, H2]: (p3(H2, H2, H2) | (~q0(I, H2) | ~k2(J2, J2)))).
% 32.52/4.54 fof(rule_299, axiom, ![C, B, D2, A2_2]: (s4(A2_2) | (~p3(B, C, D2) | ~l1(A2_2, C)))).
% 32.52/4.54 fof(rule_327, axiom, ![C2, D2]: (r5(C2, D2) | (~s4(C2) | (~k0(b) | ~n3(D2))))).
% 32.52/4.54
% 32.52/4.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 32.52/4.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 32.52/4.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 32.52/4.54 fresh(y, y, x1...xn) = u
% 32.52/4.54 C => fresh(s, t, x1...xn) = v
% 32.52/4.54 where fresh is a fresh function symbol and x1..xn are the free
% 32.52/4.54 variables of u and v.
% 32.52/4.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 32.52/4.54 input problem has no model of domain size 1).
% 32.52/4.54
% 32.52/4.54 The encoding turns the above axioms into the following unit equations and goals:
% 32.52/4.54
% 32.52/4.54 Axiom 1 (axiom_32): k0(b) = true.
% 32.52/4.55 Axiom 2 (axiom_17): q0(X, d) = true.
% 32.52/4.55 Axiom 3 (axiom_34): n0(c, d) = true.
% 32.52/4.55 Axiom 4 (axiom_19): m0(X, d, Y) = true.
% 32.52/4.55 Axiom 5 (rule_002): fresh441(X, X, Y) = true.
% 32.52/4.55 Axiom 6 (rule_107): fresh301(X, X, Y) = q1(e, Y, Y).
% 32.52/4.55 Axiom 7 (rule_107): fresh300(X, X, Y) = true.
% 32.52/4.55 Axiom 8 (rule_122): fresh279(X, X, Y) = true.
% 32.52/4.55 Axiom 9 (rule_129): fresh270(X, X, Y) = true.
% 32.52/4.55 Axiom 10 (rule_154): fresh241(X, X, Y) = true.
% 32.52/4.55 Axiom 11 (rule_240): fresh127(X, X, Y) = true.
% 32.52/4.55 Axiom 12 (rule_252): fresh108(X, X, Y) = true.
% 32.52/4.55 Axiom 13 (rule_299): fresh45(X, X, Y) = true.
% 32.52/4.55 Axiom 14 (rule_327): fresh447(X, X, Y, Z) = true.
% 32.52/4.55 Axiom 15 (rule_252): fresh109(X, X, Y, Z) = p3(Y, Y, Y).
% 32.52/4.55 Axiom 16 (rule_299): fresh46(X, X, Y, Z) = s4(Y).
% 32.52/4.55 Axiom 17 (rule_327): fresh4(X, X, Y, Z) = r5(Y, Z).
% 32.52/4.55 Axiom 18 (rule_327): fresh446(X, X, Y, Z) = fresh447(k0(b), true, Y, Z).
% 32.52/4.55 Axiom 19 (rule_002): fresh441(n0(X, Y), true, Y) = l1(Y, Y).
% 32.52/4.55 Axiom 20 (rule_327): fresh446(s4(X), true, X, Y) = fresh4(n3(Y), true, X, Y).
% 32.52/4.55 Axiom 21 (rule_107): fresh301(m0(e, d, X), true, X) = fresh300(m0(X, d, X), true, X).
% 32.52/4.55 Axiom 22 (rule_122): fresh279(m0(X, Y, X), true, X) = q1(X, X, X).
% 32.52/4.55 Axiom 23 (rule_129): fresh270(q1(X, Y, Y), true, Y) = k2(Y, Y).
% 32.52/4.55 Axiom 24 (rule_154): fresh241(q1(X, X, X), true, X) = p2(X, X, X).
% 32.52/4.55 Axiom 25 (rule_240): fresh127(p2(X, Y, Z), true, Z) = n3(Z).
% 32.52/4.55 Axiom 26 (rule_252): fresh109(k2(X, X), true, Y, Z) = fresh108(q0(Z, Y), true, Y).
% 32.52/4.55 Axiom 27 (rule_299): fresh46(p3(X, Y, Z), true, W, Y) = fresh45(l1(W, Y), true, W).
% 32.52/4.55
% 32.52/4.55 Goal 1 (prove_this): r5(d, d) = true.
% 32.52/4.55 Proof:
% 32.52/4.55 r5(d, d)
% 32.52/4.55 = { by axiom 17 (rule_327) R->L }
% 32.52/4.55 fresh4(true, true, d, d)
% 32.52/4.55 = { by axiom 11 (rule_240) R->L }
% 32.52/4.55 fresh4(fresh127(true, true, d), true, d, d)
% 32.52/4.55 = { by axiom 10 (rule_154) R->L }
% 32.52/4.55 fresh4(fresh127(fresh241(true, true, d), true, d), true, d, d)
% 32.52/4.55 = { by axiom 8 (rule_122) R->L }
% 32.52/4.55 fresh4(fresh127(fresh241(fresh279(true, true, d), true, d), true, d), true, d, d)
% 32.52/4.55 = { by axiom 4 (axiom_19) R->L }
% 32.52/4.55 fresh4(fresh127(fresh241(fresh279(m0(d, d, d), true, d), true, d), true, d), true, d, d)
% 32.52/4.55 = { by axiom 22 (rule_122) }
% 32.52/4.55 fresh4(fresh127(fresh241(q1(d, d, d), true, d), true, d), true, d, d)
% 32.52/4.55 = { by axiom 24 (rule_154) }
% 32.52/4.55 fresh4(fresh127(p2(d, d, d), true, d), true, d, d)
% 32.52/4.55 = { by axiom 25 (rule_240) }
% 32.52/4.55 fresh4(n3(d), true, d, d)
% 32.52/4.55 = { by axiom 20 (rule_327) R->L }
% 32.52/4.55 fresh446(s4(d), true, d, d)
% 32.52/4.55 = { by axiom 16 (rule_299) R->L }
% 32.52/4.55 fresh446(fresh46(true, true, d, d), true, d, d)
% 32.52/4.55 = { by axiom 12 (rule_252) R->L }
% 32.52/4.55 fresh446(fresh46(fresh108(true, true, d), true, d, d), true, d, d)
% 32.52/4.55 = { by axiom 2 (axiom_17) R->L }
% 32.52/4.55 fresh446(fresh46(fresh108(q0(X, d), true, d), true, d, d), true, d, d)
% 32.52/4.55 = { by axiom 26 (rule_252) R->L }
% 32.52/4.55 fresh446(fresh46(fresh109(k2(Y, Y), true, d, X), true, d, d), true, d, d)
% 32.52/4.55 = { by axiom 23 (rule_129) R->L }
% 32.52/4.55 fresh446(fresh46(fresh109(fresh270(q1(e, Y, Y), true, Y), true, d, X), true, d, d), true, d, d)
% 32.84/4.55 = { by axiom 6 (rule_107) R->L }
% 32.84/4.55 fresh446(fresh46(fresh109(fresh270(fresh301(true, true, Y), true, Y), true, d, X), true, d, d), true, d, d)
% 32.84/4.55 = { by axiom 4 (axiom_19) R->L }
% 32.84/4.55 fresh446(fresh46(fresh109(fresh270(fresh301(m0(e, d, Y), true, Y), true, Y), true, d, X), true, d, d), true, d, d)
% 32.84/4.55 = { by axiom 21 (rule_107) }
% 32.84/4.55 fresh446(fresh46(fresh109(fresh270(fresh300(m0(Y, d, Y), true, Y), true, Y), true, d, X), true, d, d), true, d, d)
% 32.84/4.55 = { by axiom 4 (axiom_19) }
% 32.84/4.55 fresh446(fresh46(fresh109(fresh270(fresh300(true, true, Y), true, Y), true, d, X), true, d, d), true, d, d)
% 32.84/4.55 = { by axiom 7 (rule_107) }
% 32.84/4.55 fresh446(fresh46(fresh109(fresh270(true, true, Y), true, d, X), true, d, d), true, d, d)
% 32.84/4.55 = { by axiom 9 (rule_129) }
% 32.84/4.55 fresh446(fresh46(fresh109(true, true, d, X), true, d, d), true, d, d)
% 32.84/4.55 = { by axiom 15 (rule_252) }
% 32.84/4.55 fresh446(fresh46(p3(d, d, d), true, d, d), true, d, d)
% 32.84/4.55 = { by axiom 27 (rule_299) }
% 32.84/4.55 fresh446(fresh45(l1(d, d), true, d), true, d, d)
% 32.84/4.55 = { by axiom 19 (rule_002) R->L }
% 32.84/4.55 fresh446(fresh45(fresh441(n0(c, d), true, d), true, d), true, d, d)
% 32.84/4.55 = { by axiom 3 (axiom_34) }
% 32.84/4.55 fresh446(fresh45(fresh441(true, true, d), true, d), true, d, d)
% 32.84/4.55 = { by axiom 5 (rule_002) }
% 32.84/4.55 fresh446(fresh45(true, true, d), true, d, d)
% 32.84/4.55 = { by axiom 13 (rule_299) }
% 32.84/4.55 fresh446(true, true, d, d)
% 32.84/4.55 = { by axiom 18 (rule_327) }
% 32.84/4.55 fresh447(k0(b), true, d, d)
% 32.84/4.55 = { by axiom 1 (axiom_32) }
% 32.84/4.55 fresh447(true, true, d, d)
% 32.84/4.55 = { by axiom 14 (rule_327) }
% 32.84/4.55 true
% 32.84/4.55 % SZS output end Proof
% 32.84/4.55
% 32.84/4.55 RESULT: Unsatisfiable (the axioms are contradictory).
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