%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:00:39 PM UTC 2026
% Result : Unsatisfiable 7.50s 6.62s
% Output : CNFRefutation 7.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 39 RR)
% Number of literals : 51 ( 50 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 23 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t21,axiom,
sFlat0 = compose(a,b),
introduced(definition) ).
cnf(t66,plain,
compose(a,b) = sFlat0,
inference(orient,[status(thm)],[t21]) ).
cnf(t22,axiom,
sFlat1 = codomain(compose(a,b)),
introduced(definition) ).
cnf(t273,plain,
sFlat1 = codomain(sFlat0),
inference(step,[status(thm)],[t22,t66]) ).
cnf(t82,plain,
codomain(sFlat0) = sFlat1,
inference(orient,[status(thm)],[t273]) ).
cnf(t23,axiom,
sFlat2 = codomain(a),
introduced(definition) ).
cnf(t87,plain,
codomain(a) = sFlat2,
inference(orient,[status(thm)],[t23]) ).
cnf(t19,axiom,
ifeq2(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t76,plain,
ifeq2(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(orient,[status(thm)],[t19]) ).
cnf(t17,axiom,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t60,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
cnf(t5,axiom,
compose(codomain(X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
compose(codomain(X1),X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t88,plain,
a = compose(sFlat2,a),
inference(cp,[status(thm)],[t25,t87]) ).
cnf(t114,plain,
compose(sFlat2,a) = a,
inference(orient,[status(thm)],[t88]) ).
cnf(t115,plain,
compose(sFlat2,compose(a,X1)) = compose(a,X1),
inference(cp,[status(thm)],[t60,t114]) ).
cnf(t255,plain,
compose(sFlat2,compose(a,X1)) = compose(a,X1),
inference(orient,[status(thm)],[t115]) ).
cnf(t256,plain,
compose(a,b) = compose(sFlat2,sFlat0),
inference(cp,[status(thm)],[t255,t66]) ).
cnf(t322,plain,
sFlat0 = compose(sFlat2,sFlat0),
inference(step,[status(thm)],[t256,t66]) ).
cnf(t261,plain,
compose(sFlat2,sFlat0) = sFlat0,
inference(orient,[status(thm)],[t322]) ).
cnf(t263,plain,
codomain(sFlat0) = ifeq2(there_exists(sFlat0),true,domain(sFlat2),codomain(sFlat0)),
inference(cp,[status(thm)],[t76,t261]) ).
cnf(t323,plain,
sFlat1 = ifeq2(there_exists(sFlat0),true,domain(sFlat2),codomain(sFlat0)),
inference(step,[status(thm)],[t263,t82]) ).
cnf(t6,axiom,
there_exists(compose(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t30,plain,
there_exists(compose(a,b)) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t272,plain,
there_exists(sFlat0) = true,
inference(step,[status(thm)],[t30,t66]) ).
cnf(t71,plain,
there_exists(sFlat0) = true,
inference(rw,[status(thm)],[t272]) ).
cnf(t92,plain,
there_exists(sFlat0) = true,
inference(orient,[status(thm)],[t71]) ).
cnf(t324,plain,
sFlat1 = ifeq2(true,true,domain(sFlat2),codomain(sFlat0)),
inference(step,[status(thm)],[t323,t92]) ).
cnf(t9,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t27,plain,
ifeq2(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t325,plain,
sFlat1 = domain(sFlat2),
inference(step,[status(thm)],[t324,t27]) ).
cnf(t117,plain,
codomain(a) = ifeq2(there_exists(a),true,domain(sFlat2),codomain(a)),
inference(cp,[status(thm)],[t76,t114]) ).
cnf(t279,plain,
sFlat2 = ifeq2(there_exists(a),true,domain(sFlat2),codomain(a)),
inference(step,[status(thm)],[t117,t87]) ).
cnf(hi5,axiom,
ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(hi11,axiom,
there_exists(compose(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(h1,plain,
there_exists(domain(a)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi11]) ).
cnf(hi3,axiom,
ifeq(there_exists(domain(X)),true,there_exists(X),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t0,plain,
there_exists(a) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1]) ).
cnf(t31,plain,
there_exists(a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t280,plain,
sFlat2 = ifeq2(true,true,domain(sFlat2),codomain(a)),
inference(step,[status(thm)],[t279,t31]) ).
cnf(t281,plain,
sFlat2 = domain(sFlat2),
inference(step,[status(thm)],[t280,t27]) ).
cnf(t119,plain,
domain(sFlat2) = sFlat2,
inference(orient,[status(thm)],[t281]) ).
cnf(t326,plain,
sFlat1 = sFlat2,
inference(step,[status(thm)],[t325,t119]) ).
cnf(t265,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t326]) ).
cnf(t327,plain,
codomain(a) = sFlat1,
inference(step,[status(thm)],[t87,t265]) ).
cnf(t266,plain,
codomain(a) = sFlat1,
inference(orient,[status(thm)],[t327]) ).
cnf(goal_0,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
codomain(sFlat0) != codomain(a),
inference(rw,[status(thm)],[goal_0,t66]) ).
cnf(g0_1,plain,
sFlat1 != codomain(a),
inference(rw,[status(thm)],[g0_0,t82]) ).
cnf(g0_2,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_1,t266]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.38 % Computer : n003.cluster.edu
% 0.08/5.38 % Model : x86_64 x86_64
% 0.08/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.38 % Memory : 8046.5625MB
% 0.08/5.38 % OS : Linux 6.8.0-71-generic
% 0.08/5.38 % CPULimit : 300
% 0.08/5.38 % WCLimit : 300
% 0.08/5.38 % DateTime : Fri Sep 25 06:55:58 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.50/6.62 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.50/6.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------