TSTP Solution File: SYN604-1 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : SYN604-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 : Tue May  7 08:29:46 EDT 2024

% Result   : Unsatisfiable 29.65s 5.30s
% Output   : Refutation 29.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   52
% Syntax   : Number of formulae    :  135 (  49 unt;  22 typ;   0 def)
%            Number of atoms       :  242 (  37 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives : 1140 ( 110   ~;  95   |;   0   &; 935   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  22 usr;   9 con; 0-2 aty)
%            Number of variables   :  199 (   0   ^ 199   !;   0   ?; 199   :)

% Comments : 
%------------------------------------------------------------------------------
thf(p14_type,type,
    p14: $i > $i > $o ).

thf(p9_type,type,
    p9: $i > $i > $o ).

thf(p5_type,type,
    p5: $i > $i > $o ).

thf(p3_type,type,
    p3: $i > $i > $o ).

thf(p2_type,type,
    p2: $i > $i > $o ).

thf(p15_type,type,
    p15: $i > $i > $o ).

thf(c17_type,type,
    c17: $i ).

thf(c18_type,type,
    c18: $i ).

thf(f4_type,type,
    f4: $i > $i ).

thf(f8_type,type,
    f8: $i > $i ).

thf(f12_type,type,
    f12: $i > $i ).

thf(f10_type,type,
    f10: $i > $i ).

thf(p16_type,type,
    p16: $i > $i > $o ).

thf(f11_type,type,
    f11: $i > $i ).

thf(c21_type,type,
    c21: $i ).

thf(f13_type,type,
    f13: $i > $i ).

thf(f6_type,type,
    f6: $i > $i > $i ).

thf(c22_type,type,
    c22: $i ).

thf(f7_type,type,
    f7: $i > $i > $i ).

thf(c20_type,type,
    c20: $i ).

thf(c23_type,type,
    c23: $i ).

thf(c19_type,type,
    c19: $i ).

thf(27,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p2 @ ( f6 @ A @ B ) @ ( f6 @ C @ D ) )
      | ~ ( p2 @ B @ D )
      | ~ ( p5 @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_27) ).

thf(56,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p2 @ ( f6 @ A @ B ) @ ( f6 @ C @ D ) )
      | ~ ( p2 @ B @ D )
      | ~ ( p5 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(10,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p16 @ A @ B )
      | ( p16 @ B @ ( f12 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_10) ).

thf(32,plain,
    ! [B: $i,A: $i] :
      ( ( p16 @ A @ B )
      | ( p16 @ B @ ( f12 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(72,plain,
    ! [B: $i,A: $i] :
      ( ( p16 @ A @ B )
      | ( p16 @ B @ ( f12 @ A ) ) ),
    inference(cnf,[status(esa)],[32]) ).

thf(29,negated_conjecture,
    ! [A: $i] :
      ( ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ c23 ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ A ) ) )
      | ~ ( p16 @ ( f4 @ A ) @ ( f12 @ c19 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_29) ).

thf(52,plain,
    ! [A: $i] :
      ( ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ c23 ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ A ) ) )
      | ~ ( p16 @ ( f4 @ A ) @ ( f12 @ c19 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(62,plain,
    ! [A: $i] :
      ( ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ c23 ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ A ) ) )
      | ~ ( p16 @ ( f4 @ A ) @ ( f12 @ c19 ) ) ),
    inference(cnf,[status(esa)],[52]) ).

thf(28,negated_conjecture,
    ! [A: $i] :
      ~ ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ A ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ ( f13 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p16_28) ).

thf(53,plain,
    ! [A: $i] :
      ~ ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ A ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ ( f13 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(64,plain,
    ! [A: $i] :
      ~ ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ A ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ ( f13 @ A ) ) ) ),
    inference(polarity_switch,[status(thm)],[53]) ).

thf(200,plain,
    ! [B: $i,A: $i] :
      ( ~ ( p16 @ ( f4 @ A ) @ ( f12 @ c19 ) )
      | ( ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ c23 ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ A ) ) )
       != ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ B ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ ( f13 @ B ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[62,64]) ).

thf(201,plain,
    ~ ( p16 @ ( f4 @ ( f13 @ c23 ) ) @ ( f12 @ c19 ) ),
    inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( f13 @ c23 )),bind(B,$thf( c23 ))]]) ).

thf(218,plain,
    ! [B: $i,A: $i] :
      ( ( p16 @ B @ ( f12 @ A ) )
      | ( ( p16 @ A @ B )
       != ( p16 @ ( f4 @ ( f13 @ c23 ) ) @ ( f12 @ c19 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[72,201]) ).

thf(219,plain,
    p16 @ ( f12 @ c19 ) @ ( f12 @ ( f4 @ ( f13 @ c23 ) ) ),
    inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( f4 @ ( f13 @ c23 ) )),bind(B,$thf( f12 @ c19 ))]]) ).

thf(235,plain,
    ( ( p16 @ ( f12 @ c19 ) @ ( f12 @ ( f4 @ ( f13 @ c23 ) ) ) )
   != ( p16 @ ( f4 @ ( f13 @ c23 ) ) @ ( f12 @ c19 ) ) ),
    inference(paramod_ordered,[status(thm)],[219,201]) ).

thf(238,plain,
    ( ( ( f12 @ c19 )
     != ( f4 @ ( f13 @ c23 ) ) )
    | ( ( f12 @ ( f4 @ ( f13 @ c23 ) ) )
     != ( f12 @ c19 ) ) ),
    inference(simp,[status(thm)],[235]) ).

thf(15,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p3 @ ( f12 @ A ) @ ( f12 @ B ) )
      | ~ ( p3 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_15) ).

thf(48,plain,
    ! [B: $i,A: $i] :
      ( ( p3 @ ( f12 @ A ) @ ( f12 @ B ) )
      | ~ ( p3 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(65,plain,
    ! [B: $i,A: $i] :
      ( ( p3 @ ( f12 @ A ) @ ( f12 @ B ) )
      | ~ ( p3 @ A @ B ) ),
    inference(cnf,[status(esa)],[48]) ).

thf(7,negated_conjecture,
    ! [A: $i] : ( p3 @ ( f4 @ ( f8 @ A ) ) @ ( f12 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_7) ).

thf(41,plain,
    ! [A: $i] : ( p3 @ ( f4 @ ( f8 @ A ) ) @ ( f12 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(129,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ ( f12 @ B ) @ ( f12 @ C ) )
      | ( ( p3 @ ( f4 @ ( f8 @ A ) ) @ ( f12 @ A ) )
       != ( p3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[41,65]) ).

thf(130,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) @ ( f12 @ ( f12 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[129:[bind(A,$thf( F )),bind(B,$thf( f4 @ ( f8 @ F ) )),bind(C,$thf( f12 @ F ))]]) ).

thf(134,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) @ ( f12 @ ( f12 @ A ) ) ),
    inference(simp,[status(thm)],[130]) ).

thf(23,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( p16 @ A @ B )
      | ~ ( p16 @ A @ C )
      | ~ ( p16 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_23) ).

thf(58,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p16 @ A @ B )
      | ~ ( p16 @ A @ C )
      | ~ ( p16 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(17,negated_conjecture,
    ! [A: $i] : ( p16 @ ( f4 @ ( f6 @ c18 @ c22 ) ) @ ( f4 @ ( f6 @ c18 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_17) ).

thf(39,plain,
    ! [A: $i] : ( p16 @ ( f4 @ ( f6 @ c18 @ c22 ) ) @ ( f4 @ ( f6 @ c18 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(93,plain,
    ! [B: $i,A: $i] :
      ( ( p16 @ ( f4 @ ( f6 @ c18 @ c22 ) ) @ ( f4 @ ( f6 @ c18 @ A ) ) )
     != ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ B ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ ( f13 @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[39,64]) ).

thf(94,plain,
    ! [B: $i,A: $i] :
      ( ( ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ B ) )
       != ( f4 @ ( f6 @ c18 @ c22 ) ) )
      | ( ( f4 @ ( f6 @ c18 @ A ) )
       != ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ ( f13 @ B ) ) ) ) ),
    inference(simp,[status(thm)],[93]) ).

thf(3,negated_conjecture,
    ! [A: $i] : ( p5 @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_3) ).

thf(42,plain,
    ! [A: $i] : ( p5 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(13,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p2 @ ( f8 @ A ) @ ( f8 @ B ) )
      | ~ ( p3 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_13) ).

thf(37,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ ( f8 @ A ) @ ( f8 @ B ) )
      | ~ ( p3 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(8,negated_conjecture,
    ! [A: $i] : ( p3 @ ( f12 @ ( f10 @ A ) ) @ ( f10 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_8) ).

thf(46,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f10 @ A ) ) @ ( f10 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(125,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ ( f12 @ B ) @ ( f12 @ C ) )
      | ( ( p3 @ ( f12 @ ( f10 @ A ) ) @ ( f10 @ A ) )
       != ( p3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[46,65]) ).

thf(126,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) @ ( f12 @ ( f10 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( F )),bind(B,$thf( f12 @ ( f10 @ F ) )),bind(C,$thf( f10 @ F ))]]) ).

thf(135,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) @ ( f12 @ ( f10 @ A ) ) ),
    inference(simp,[status(thm)],[126]) ).

thf(149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ ( f12 @ B ) @ ( f12 @ C ) )
      | ( ( p3 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) @ ( f12 @ ( f10 @ A ) ) )
       != ( p3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[135,65]) ).

thf(150,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( H )),bind(B,$thf( f12 @ ( f12 @ ( f10 @ H ) ) )),bind(C,$thf( f12 @ ( f10 @ H ) ))]]) ).

thf(151,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ),
    inference(simp,[status(thm)],[150]) ).

thf(155,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ ( f12 @ B ) @ ( f12 @ C ) )
      | ( ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) )
       != ( p3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[151,65]) ).

thf(156,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( J )),bind(B,$thf( f12 @ ( f12 @ ( f12 @ ( f10 @ J ) ) ) )),bind(C,$thf( f12 @ ( f12 @ ( f10 @ J ) ) ))]]) ).

thf(157,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) ),
    inference(simp,[status(thm)],[156]) ).

thf(26,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p5 @ ( f7 @ A @ B ) @ ( f7 @ C @ D ) )
      | ~ ( p2 @ A @ C )
      | ~ ( p5 @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_26) ).

thf(57,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p5 @ ( f7 @ A @ B ) @ ( f7 @ C @ D ) )
      | ~ ( p2 @ A @ C )
      | ~ ( p5 @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(61,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p2 @ ( f6 @ A @ B ) @ ( f6 @ C @ D ) )
      | ~ ( p2 @ B @ D )
      | ~ ( p5 @ A @ C ) ),
    inference(cnf,[status(esa)],[56]) ).

thf(220,plain,
    ! [B: $i,A: $i] :
      ( ( p16 @ A @ B )
      | ( ( p16 @ B @ ( f12 @ A ) )
       != ( p16 @ ( f4 @ ( f13 @ c23 ) ) @ ( f12 @ c19 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[72,201]) ).

thf(221,plain,
    p16 @ c19 @ ( f4 @ ( f13 @ c23 ) ),
    inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( c19 )),bind(B,$thf( f4 @ ( f13 @ c23 ) ))]]) ).

thf(9,negated_conjecture,
    ! [A: $i] : ( p16 @ ( f10 @ ( f11 @ c21 ) ) @ ( f12 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_9) ).

thf(36,plain,
    ! [A: $i] : ( p16 @ ( f10 @ ( f11 @ c21 ) ) @ ( f12 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(88,plain,
    ! [B: $i,A: $i] :
      ( ( p16 @ ( f10 @ ( f11 @ c21 ) ) @ ( f12 @ A ) )
     != ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ B ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ ( f13 @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[36,64]) ).

thf(89,plain,
    ! [B: $i,A: $i] :
      ( ( ( f10 @ ( f11 @ c21 ) )
       != ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ B ) ) )
      | ( ( f12 @ A )
       != ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ ( f13 @ B ) ) ) ) ),
    inference(simp,[status(thm)],[88]) ).

thf(19,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( p9 @ A @ B )
      | ~ ( p9 @ C @ A )
      | ~ ( p9 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_19) ).

thf(60,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p9 @ A @ B )
      | ~ ( p9 @ C @ A )
      | ~ ( p9 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(97,plain,
    ! [B: $i,A: $i] :
      ( ( p16 @ A @ B )
      | ( ( p16 @ B @ ( f12 @ A ) )
       != ( p16 @ A @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[72]) ).

thf(100,plain,
    ! [B: $i,A: $i] :
      ( ( p16 @ A @ B )
      | ( B != A )
      | ( ( f12 @ A )
       != B ) ),
    inference(simp,[status(thm)],[97]) ).

thf(102,plain,
    ! [A: $i] :
      ( ( p16 @ A @ A )
      | ( ( f12 @ A )
       != A ) ),
    inference(simp,[status(thm)],[100]) ).

thf(2,negated_conjecture,
    ! [A: $i] : ( p9 @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_2) ).

thf(38,plain,
    ! [A: $i] : ( p9 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(137,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ ( f12 @ B ) @ ( f12 @ C ) )
      | ( ( p3 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) @ ( f12 @ ( f12 @ A ) ) )
       != ( p3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[134,65]) ).

thf(138,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( H )),bind(B,$thf( f12 @ ( f4 @ ( f8 @ H ) ) )),bind(C,$thf( f12 @ ( f12 @ H ) ))]]) ).

thf(139,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ A ) ) ) ),
    inference(simp,[status(thm)],[138]) ).

thf(152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ ( f12 @ B ) @ ( f12 @ C ) )
      | ( ( p3 @ ( f12 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ A ) ) ) )
       != ( p3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[139,65]) ).

thf(153,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ A ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( J )),bind(B,$thf( f12 @ ( f12 @ ( f4 @ ( f8 @ J ) ) ) )),bind(C,$thf( f12 @ ( f12 @ ( f12 @ J ) ) ))]]) ).

thf(154,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ A ) ) ) ) ),
    inference(simp,[status(thm)],[153]) ).

thf(158,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ ( f12 @ B ) @ ( f12 @ C ) )
      | ( ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ A ) ) ) ) )
       != ( p3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[154,65]) ).

thf(159,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ A ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( L )),bind(B,$thf( f12 @ ( f12 @ ( f12 @ ( f4 @ ( f8 @ L ) ) ) ) )),bind(C,$thf( f12 @ ( f12 @ ( f12 @ ( f12 @ L ) ) ) ))]]) ).

thf(160,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f4 @ ( f8 @ A ) ) ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ A ) ) ) ) ) ),
    inference(simp,[status(thm)],[159]) ).

thf(14,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p3 @ ( f10 @ A ) @ ( f10 @ B ) )
      | ~ ( p9 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_14) ).

thf(33,plain,
    ! [B: $i,A: $i] :
      ( ( p3 @ ( f10 @ A ) @ ( f10 @ B ) )
      | ~ ( p9 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(11,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p9 @ ( f11 @ A ) @ ( f11 @ B ) )
      | ~ ( p9 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9_11) ).

thf(45,plain,
    ! [B: $i,A: $i] :
      ( ( p9 @ ( f11 @ A ) @ ( f11 @ B ) )
      | ~ ( p9 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(1,negated_conjecture,
    ! [A: $i] : ( p14 @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14_1) ).

thf(34,plain,
    ! [A: $i] : ( p14 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(16,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p3 @ ( f4 @ A ) @ ( f4 @ B ) )
      | ~ ( p2 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_16) ).

thf(44,plain,
    ! [B: $i,A: $i] :
      ( ( p3 @ ( f4 @ A ) @ ( f4 @ B ) )
      | ~ ( p2 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(30,negated_conjecture,
    ! [A: $i] :
      ( ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ ( f8 @ ( f10 @ ( f11 @ c21 ) ) ) ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ A ) ) )
      | ~ ( p16 @ c19 @ ( f4 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_30) ).

thf(59,plain,
    ! [A: $i] :
      ( ( p16 @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ ( f8 @ ( f10 @ ( f11 @ c21 ) ) ) ) ) @ ( f4 @ ( f6 @ ( f7 @ c20 @ c18 ) @ A ) ) )
      | ~ ( p16 @ c19 @ ( f4 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(21,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ B )
      | ~ ( p3 @ C @ A )
      | ~ ( p3 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_21) ).

thf(54,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ A @ B )
      | ~ ( p3 @ C @ A )
      | ~ ( p3 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(24,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p15 @ A @ B )
      | ~ ( p15 @ C @ D )
      | ~ ( p5 @ D @ B )
      | ~ ( p14 @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_24) ).

thf(49,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p15 @ A @ B )
      | ~ ( p15 @ C @ D )
      | ~ ( p5 @ D @ B )
      | ~ ( p14 @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(76,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p15 @ A @ B )
      | ~ ( p15 @ C @ D )
      | ~ ( p5 @ D @ B )
      | ~ ( p14 @ C @ A ) ),
    inference(cnf,[status(esa)],[49]) ).

thf(196,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p3 @ ( f12 @ B ) @ ( f12 @ C ) )
      | ( ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) )
       != ( p3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[157,65]) ).

thf(197,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( L )),bind(B,$thf( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ L ) ) ) ) )),bind(C,$thf( f12 @ ( f12 @ ( f12 @ ( f10 @ L ) ) ) ))]]) ).

thf(198,plain,
    ! [A: $i] : ( p3 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) ) ) @ ( f12 @ ( f12 @ ( f12 @ ( f12 @ ( f10 @ A ) ) ) ) ) ),
    inference(simp,[status(thm)],[197]) ).

thf(108,plain,
    ! [B: $i,A: $i] :
      ( ( ( f6 @ ( f7 @ c20 @ c18 ) @ B )
       != ( f6 @ c18 @ c22 ) )
      | ( ( f6 @ c18 @ A )
       != ( f6 @ ( f7 @ c20 @ c18 ) @ ( f13 @ B ) ) ) ),
    inference(simp,[status(thm)],[94]) ).

thf(6,negated_conjecture,
    p15 @ c17 @ c18,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_6) ).

thf(35,plain,
    p15 @ c17 @ c18,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(25,negated_conjecture,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p16 @ A @ B )
      | ~ ( p3 @ C @ A )
      | ~ ( p3 @ D @ B )
      | ~ ( p16 @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_25) ).

thf(50,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( p16 @ A @ B )
      | ~ ( p3 @ C @ A )
      | ~ ( p3 @ D @ B )
      | ~ ( p16 @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(163,plain,
    ! [B: $i,A: $i] :
      ( ( ( f7 @ c20 @ c18 )
       != c18 )
      | ( B != c22 )
      | ( ( f7 @ c20 @ c18 )
       != c18 )
      | ( A
       != ( f13 @ B ) ) ),
    inference(simp,[status(thm)],[108]) ).

thf(182,plain,
    ( ( f7 @ c20 @ c18 )
   != c18 ),
    inference(simp,[status(thm)],[163]) ).

thf(5,negated_conjecture,
    ! [A: $i] : ( p2 @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_5) ).

thf(31,plain,
    ! [A: $i] : ( p2 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(18,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( p14 @ A @ B )
      | ~ ( p14 @ C @ A )
      | ~ ( p14 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14_18) ).

thf(43,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p14 @ A @ B )
      | ~ ( p14 @ C @ A )
      | ~ ( p14 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(12,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ( p2 @ ( f13 @ A ) @ ( f13 @ B ) )
      | ~ ( p2 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).

thf(40,plain,
    ! [B: $i,A: $i] :
      ( ( p2 @ ( f13 @ A ) @ ( f13 @ B ) )
      | ~ ( p2 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(22,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ B )
      | ~ ( p2 @ C @ A )
      | ~ ( p2 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_22) ).

thf(55,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p2 @ A @ B )
      | ~ ( p2 @ C @ A )
      | ~ ( p2 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(20,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( p5 @ A @ B )
      | ~ ( p5 @ C @ A )
      | ~ ( p5 @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_20) ).

thf(51,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p5 @ A @ B )
      | ~ ( p5 @ C @ A )
      | ~ ( p5 @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(4,negated_conjecture,
    ! [A: $i] : ( p3 @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_4) ).

thf(47,plain,
    ! [A: $i] : ( p3 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(222,plain,
    ! [A: $i] :
      ( ( p16 @ ( f10 @ ( f11 @ c21 ) ) @ ( f12 @ A ) )
     != ( p16 @ ( f4 @ ( f13 @ c23 ) ) @ ( f12 @ c19 ) ) ),
    inference(paramod_ordered,[status(thm)],[36,201]) ).

thf(227,plain,
    ! [A: $i] :
      ( ( ( f10 @ ( f11 @ c21 ) )
       != ( f4 @ ( f13 @ c23 ) ) )
      | ( ( f12 @ A )
       != ( f12 @ c19 ) ) ),
    inference(simp,[status(thm)],[222]) ).

thf(229,plain,
    ( ( p16 @ ( f4 @ ( f13 @ c23 ) ) @ ( f12 @ c19 ) )
   != ( p16 @ c19 @ ( f4 @ ( f13 @ c23 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[221,201]) ).

thf(232,plain,
    ( ( ( f4 @ ( f13 @ c23 ) )
     != c19 )
    | ( ( f12 @ c19 )
     != ( f4 @ ( f13 @ c23 ) ) ) ),
    inference(simp,[status(thm)],[229]) ).

thf(1595,plain,
    $false,
    inference(e,[status(thm)],[56,238,65,53,41,134,48,58,94,42,37,52,157,46,57,61,221,89,60,201,102,38,160,33,45,64,32,34,44,59,54,49,219,76,39,198,108,135,35,50,182,31,154,72,43,40,55,139,151,36,51,47,62,227,232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN604-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n002.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 13:38:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.90/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.25/0.94  % [INFO] 	 Parsing done (119ms). 
% 1.25/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.62/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.62/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.62/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.93/1.26  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 2.17/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.17/1.32  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.17/1.32  % [INFO] 	 Type checking passed. 
% 2.17/1.32  % [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 ... 
% 29.65/5.30  % External prover 'e' found a proof!
% 29.65/5.30  % [INFO] 	 Killing All external provers ... 
% 29.65/5.30  % Time passed: 4772ms (effective reasoning time: 4349ms)
% 29.65/5.30  % Solved by 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)>
% 29.65/5.30  % Axioms used in derivation (0): 
% 29.65/5.30  % No. of inferences in proof: 113
% 29.65/5.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4772 ms resp. 4349 ms w/o parsing
% 29.65/5.34  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.65/5.35  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------