TSTP Solution File: GRP123-7.003 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : GRP123-7.003 : TPTP v8.2.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 : Mon May 20 21:03:12 EDT 2024

% Result   : Unsatisfiable 24.33s 4.87s
% Output   : Refutation 24.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   93 (  27 unt;   7 typ;   0 def)
%            Number of atoms       :  234 (  16 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  745 (  89   ~; 116   |;   0   &; 540   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :  136 (   0   ^ 136   !;   0   ?; 136   :)

% Comments : 
%------------------------------------------------------------------------------
thf(product1_type,type,
    product1: $i > $i > $i > $o ).

thf(product2_type,type,
    product2: $i > $i > $i > $o ).

thf(group_element_type,type,
    group_element: $i > $o ).

thf(e_1_type,type,
    e_1: $i ).

thf(equalish_type,type,
    equalish: $i > $i > $o ).

thf(e_3_type,type,
    e_3: $i ).

thf(e_2_type,type,
    e_2: $i ).

thf(2,axiom,
    group_element @ e_1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).

thf(29,plain,
    group_element @ e_1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(21,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( group_element @ A )
      | ~ ( group_element @ B )
      | ( product1 @ A @ B @ e_1 )
      | ( product1 @ A @ B @ e_2 )
      | ( product1 @ A @ B @ e_3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).

thf(58,plain,
    ! [B: $i,A: $i] :
      ( ~ ( group_element @ A )
      | ~ ( group_element @ B )
      | ( product1 @ A @ B @ e_1 )
      | ( product1 @ A @ B @ e_2 )
      | ( product1 @ A @ B @ e_3 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(59,plain,
    ! [B: $i,A: $i] :
      ( ~ ( group_element @ A )
      | ~ ( group_element @ B )
      | ( product1 @ A @ B @ e_1 )
      | ( product1 @ A @ B @ e_2 )
      | ( product1 @ A @ B @ e_3 ) ),
    inference(cnf,[status(esa)],[58]) ).

thf(17,axiom,
    ! [A: $i] : ( product1 @ A @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).

thf(51,plain,
    ! [A: $i] : ( product1 @ A @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(1,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ C )
      | ~ ( product1 @ C @ B @ D )
      | ( product2 @ D @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).

thf(27,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ C )
      | ~ ( product1 @ C @ B @ D )
      | ( product2 @ D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(28,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ C )
      | ~ ( product1 @ C @ B @ D )
      | ( product2 @ D @ A @ B ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(76,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ B @ C @ D )
      | ( product2 @ E @ B @ C )
      | ( ( product1 @ A @ A @ A )
       != ( product1 @ D @ C @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[51,28]) ).

thf(77,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product1 @ B @ A @ A )
      | ( product2 @ A @ B @ A ) ),
    inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).

thf(105,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( group_element @ A )
      | ~ ( group_element @ B )
      | ( product1 @ A @ B @ e_1 )
      | ( product1 @ A @ B @ e_3 )
      | ( product2 @ C @ D @ C )
      | ( ( product1 @ A @ B @ e_2 )
       != ( product1 @ D @ C @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[59,77]) ).

thf(106,plain,
    ! [A: $i] :
      ( ~ ( group_element @ A )
      | ~ ( group_element @ e_2 )
      | ( product1 @ A @ e_2 @ e_1 )
      | ( product1 @ A @ e_2 @ e_3 )
      | ( product2 @ e_2 @ A @ e_2 ) ),
    inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( A )),bind(B,$thf( e_2 )),bind(C,$thf( e_2 )),bind(D,$thf( A ))]]) ).

thf(7,axiom,
    group_element @ e_2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).

thf(36,plain,
    group_element @ e_2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(143,plain,
    ! [A: $i] :
      ( ~ ( group_element @ A )
      | ~ $true
      | ( product1 @ A @ e_2 @ e_1 )
      | ( product1 @ A @ e_2 @ e_3 )
      | ( product2 @ e_2 @ A @ e_2 ) ),
    inference(rewrite,[status(thm)],[106,36]) ).

thf(144,plain,
    ! [A: $i] :
      ( ~ ( group_element @ A )
      | ( product1 @ A @ e_2 @ e_1 )
      | ( product1 @ A @ e_2 @ e_3 )
      | ( product2 @ e_2 @ A @ e_2 ) ),
    inference(simp,[status(thm)],[143]) ).

thf(145,plain,
    ! [A: $i] :
      ( ( product1 @ A @ e_2 @ e_1 )
      | ( product1 @ A @ e_2 @ e_3 )
      | ( product2 @ e_2 @ A @ e_2 )
      | ( ( group_element @ e_1 )
       != ( group_element @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29,144]) ).

thf(146,plain,
    ( ( product1 @ e_1 @ e_2 @ e_1 )
    | ( product1 @ e_1 @ e_2 @ e_3 )
    | ( product2 @ e_2 @ e_1 @ e_2 ) ),
    inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( e_1 ))]]) ).

thf(69,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ C )
      | ( product2 @ D @ A @ B )
      | ( ( product1 @ C @ B @ D )
       != ( product1 @ A @ B @ C ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[28]) ).

thf(70,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product1 @ B @ A @ B )
      | ( product2 @ B @ B @ A ) ),
    inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).

thf(71,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product1 @ B @ A @ B )
      | ( product2 @ B @ B @ A ) ),
    inference(simp,[status(thm)],[70]) ).

thf(72,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( product2 @ C @ C @ B )
      | ( ( product1 @ A @ A @ A )
       != ( product1 @ C @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[51,71]) ).

thf(73,plain,
    ! [A: $i] : ( product2 @ A @ A @ A ),
    inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product2 @ A @ B @ C )
      | ~ ( product2 @ A @ D @ C )
      | ( equalish @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_right_cancellation) ).

thf(66,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product2 @ A @ B @ C )
      | ~ ( product2 @ A @ D @ C )
      | ( equalish @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(67,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product2 @ A @ B @ C )
      | ~ ( product2 @ A @ D @ C )
      | ( equalish @ B @ D ) ),
    inference(cnf,[status(esa)],[66]) ).

thf(896,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product2 @ B @ E @ D )
      | ( equalish @ C @ E )
      | ( ( product2 @ A @ A @ A )
       != ( product2 @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[73,67]) ).

thf(897,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product2 @ A @ B @ A )
      | ( equalish @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[896:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).

thf(936,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product2 @ A @ B @ A )
      | ( equalish @ A @ B ) ),
    inference(simp,[status(thm)],[897]) ).

thf(1184,plain,
    ! [B: $i,A: $i] :
      ( ( product1 @ e_1 @ e_2 @ e_1 )
      | ( product1 @ e_1 @ e_2 @ e_3 )
      | ( equalish @ A @ B )
      | ( ( product2 @ e_2 @ e_1 @ e_2 )
       != ( product2 @ A @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[146,936]) ).

thf(1185,plain,
    ( ( product1 @ e_1 @ e_2 @ e_1 )
    | ( product1 @ e_1 @ e_2 @ e_3 )
    | ( equalish @ e_2 @ e_1 ) ),
    inference(pattern_uni,[status(thm)],[1184:[bind(A,$thf( e_2 )),bind(B,$thf( e_1 ))]]) ).

thf(13,axiom,
    ~ ( equalish @ e_2 @ e_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

thf(44,plain,
    ~ ( equalish @ e_2 @ e_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(45,plain,
    ~ ( equalish @ e_2 @ e_1 ),
    inference(polarity_switch,[status(thm)],[44]) ).

thf(2258,plain,
    ( ( product1 @ e_1 @ e_2 @ e_1 )
    | ( product1 @ e_1 @ e_2 @ e_3 )
    | $false ),
    inference(rewrite,[status(thm)],[1185,45]) ).

thf(2259,plain,
    ( ( product1 @ e_1 @ e_2 @ e_1 )
    | ( product1 @ e_1 @ e_2 @ e_3 ) ),
    inference(simp,[status(thm)],[2258]) ).

thf(4,axiom,
    group_element @ e_3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).

thf(32,plain,
    group_element @ e_3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(147,plain,
    ! [A: $i] :
      ( ( product1 @ A @ e_2 @ e_1 )
      | ( product1 @ A @ e_2 @ e_3 )
      | ( product2 @ e_2 @ A @ e_2 )
      | ( ( group_element @ e_3 )
       != ( group_element @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[32,144]) ).

thf(148,plain,
    ( ( product1 @ e_3 @ e_2 @ e_1 )
    | ( product1 @ e_3 @ e_2 @ e_3 )
    | ( product2 @ e_2 @ e_3 @ e_2 ) ),
    inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( e_3 ))]]) ).

thf(1178,plain,
    ! [B: $i,A: $i] :
      ( ( product1 @ e_3 @ e_2 @ e_1 )
      | ( product1 @ e_3 @ e_2 @ e_3 )
      | ( equalish @ A @ B )
      | ( ( product2 @ e_2 @ e_3 @ e_2 )
       != ( product2 @ A @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[148,936]) ).

thf(1179,plain,
    ( ( product1 @ e_3 @ e_2 @ e_1 )
    | ( product1 @ e_3 @ e_2 @ e_3 )
    | ( equalish @ e_2 @ e_3 ) ),
    inference(pattern_uni,[status(thm)],[1178:[bind(A,$thf( e_2 )),bind(B,$thf( e_3 ))]]) ).

thf(15,axiom,
    ~ ( equalish @ e_2 @ e_3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

thf(47,plain,
    ~ ( equalish @ e_2 @ e_3 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(48,plain,
    ~ ( equalish @ e_2 @ e_3 ),
    inference(polarity_switch,[status(thm)],[47]) ).

thf(1187,plain,
    ( ( product1 @ e_3 @ e_2 @ e_1 )
    | ( product1 @ e_3 @ e_2 @ e_3 )
    | $false ),
    inference(rewrite,[status(thm)],[1179,48]) ).

thf(1188,plain,
    ( ( product1 @ e_3 @ e_2 @ e_1 )
    | ( product1 @ e_3 @ e_2 @ e_3 ) ),
    inference(simp,[status(thm)],[1187]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ C )
      | ~ ( product1 @ A @ D @ C )
      | ( equalish @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).

thf(62,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ C )
      | ~ ( product1 @ A @ D @ C )
      | ( equalish @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(63,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ C )
      | ~ ( product1 @ A @ D @ C )
      | ( equalish @ B @ D ) ),
    inference(cnf,[status(esa)],[62]) ).

thf(635,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ B @ E @ D )
      | ( equalish @ C @ E )
      | ( ( product1 @ A @ A @ A )
       != ( product1 @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[51,63]) ).

thf(636,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ A )
      | ( equalish @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[635:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).

thf(644,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ A )
      | ( equalish @ A @ B ) ),
    inference(simp,[status(thm)],[636]) ).

thf(1196,plain,
    ! [B: $i,A: $i] :
      ( ( product1 @ e_3 @ e_2 @ e_1 )
      | ( equalish @ A @ B )
      | ( ( product1 @ e_3 @ e_2 @ e_3 )
       != ( product1 @ A @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1188,644]) ).

thf(1197,plain,
    ( ( product1 @ e_3 @ e_2 @ e_1 )
    | ( equalish @ e_3 @ e_2 ) ),
    inference(pattern_uni,[status(thm)],[1196:[bind(A,$thf( e_3 )),bind(B,$thf( e_2 ))]]) ).

thf(16,axiom,
    ~ ( equalish @ e_3 @ e_2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

thf(49,plain,
    ~ ( equalish @ e_3 @ e_2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(50,plain,
    ~ ( equalish @ e_3 @ e_2 ),
    inference(polarity_switch,[status(thm)],[49]) ).

thf(1338,plain,
    ( ( product1 @ e_3 @ e_2 @ e_1 )
    | $false ),
    inference(rewrite,[status(thm)],[1197,50]) ).

thf(1339,plain,
    product1 @ e_3 @ e_2 @ e_1,
    inference(simp,[status(thm)],[1338]) ).

thf(1367,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ C )
      | ( product2 @ D @ A @ B )
      | ( ( product1 @ e_3 @ e_2 @ e_1 )
       != ( product1 @ C @ B @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1339,28]) ).

thf(1368,plain,
    ! [A: $i] :
      ( ~ ( product1 @ A @ e_2 @ e_3 )
      | ( product2 @ e_1 @ A @ e_2 ) ),
    inference(pattern_uni,[status(thm)],[1367:[bind(A,$thf( A )),bind(B,$thf( e_2 )),bind(C,$thf( e_3 )),bind(D,$thf( e_1 ))]]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product2 @ A @ B @ C )
      | ~ ( product2 @ A @ B @ D )
      | ( equalish @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).

thf(54,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product2 @ A @ B @ C )
      | ~ ( product2 @ A @ B @ D )
      | ( equalish @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(55,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product2 @ A @ B @ C )
      | ~ ( product2 @ A @ B @ D )
      | ( equalish @ C @ D ) ),
    inference(cnf,[status(esa)],[54]) ).

thf(192,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product2 @ B @ C @ E )
      | ( equalish @ D @ E )
      | ( ( product2 @ A @ A @ A )
       != ( product2 @ B @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[73,55]) ).

thf(193,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product2 @ A @ A @ B )
      | ( equalish @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).

thf(228,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product2 @ A @ A @ B )
      | ( equalish @ A @ B ) ),
    inference(simp,[status(thm)],[193]) ).

thf(3217,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ A @ e_2 @ e_3 )
      | ( equalish @ B @ C )
      | ( ( product2 @ e_1 @ A @ e_2 )
       != ( product2 @ B @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1368,228]) ).

thf(3218,plain,
    ( ~ ( product1 @ e_1 @ e_2 @ e_3 )
    | ( equalish @ e_1 @ e_2 ) ),
    inference(pattern_uni,[status(thm)],[3217:[bind(A,$thf( e_1 )),bind(B,$thf( e_1 )),bind(C,$thf( e_2 ))]]) ).

thf(5,axiom,
    ~ ( equalish @ e_1 @ e_2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

thf(33,plain,
    ~ ( equalish @ e_1 @ e_2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(34,plain,
    ~ ( equalish @ e_1 @ e_2 ),
    inference(polarity_switch,[status(thm)],[33]) ).

thf(3405,plain,
    ( ~ ( product1 @ e_1 @ e_2 @ e_3 )
    | $false ),
    inference(rewrite,[status(thm)],[3218,34]) ).

thf(3406,plain,
    ~ ( product1 @ e_1 @ e_2 @ e_3 ),
    inference(simp,[status(thm)],[3405]) ).

thf(3407,plain,
    ( ( product1 @ e_1 @ e_2 @ e_1 )
    | $false ),
    inference(rewrite,[status(thm)],[2259,3406]) ).

thf(3408,plain,
    product1 @ e_1 @ e_2 @ e_1,
    inference(simp,[status(thm)],[3407]) ).

thf(637,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product1 @ B @ C @ D )
      | ( equalish @ C @ E )
      | ( ( product1 @ A @ A @ A )
       != ( product1 @ B @ E @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[51,63]) ).

thf(638,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ A )
      | ( equalish @ B @ A ) ),
    inference(pattern_uni,[status(thm)],[637:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( A ))]]) ).

thf(645,plain,
    ! [B: $i,A: $i] :
      ( ~ ( product1 @ A @ B @ A )
      | ( equalish @ B @ A ) ),
    inference(simp,[status(thm)],[638]) ).

thf(3662,plain,
    ! [B: $i,A: $i] :
      ( ( equalish @ B @ A )
      | ( ( product1 @ e_1 @ e_2 @ e_1 )
       != ( product1 @ A @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3408,645]) ).

thf(3663,plain,
    equalish @ e_2 @ e_1,
    inference(pattern_uni,[status(thm)],[3662:[bind(A,$thf( e_1 )),bind(B,$thf( e_2 ))]]) ).

thf(3859,plain,
    $false,
    inference(rewrite,[status(thm)],[3663,45]) ).

thf(3860,plain,
    $false,
    inference(simp,[status(thm)],[3859]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP123-7.003 : TPTP v8.2.0. Released v1.2.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n020.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 04:38:54 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.06/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/1.08  % [INFO] 	 Parsing done (127ms). 
% 1.44/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.30  % [INFO] 	 nitpick registered as external prover. 
% 1.68/1.30  % [INFO] 	 Scanning for conjecture ... 
% 1.94/1.38  % [INFO] 	 Found a conjecture (or negated_conjecture) and 25 axioms. Running axiom selection ... 
% 2.07/1.46  % [INFO] 	 Axiom selection finished. Selected 25 axioms (removed 0 axioms). 
% 2.23/1.49  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.23/1.49  % [INFO] 	 Type checking passed. 
% 2.23/1.50  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 24.33/4.86  % [INFO] 	 Killing All external provers ... 
% 24.33/4.87  % Time passed: 4352ms (effective reasoning time: 3776ms)
% 24.33/4.87  % Axioms used in derivation (12): e_3_is_not_e_2, element_2, product1_idempotence, product1_total_function1, e_1_is_not_e_2, product2_total_function2, e_2_is_not_e_3, element_3, e_2_is_not_e_1, product2_right_cancellation, product1_right_cancellation, element_1
% 24.33/4.87  % No. of inferences in proof: 86
% 24.33/4.87  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4352 ms resp. 3776 ms w/o parsing
% 24.33/4.93  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.33/4.93  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------