%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP181-3 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 04:24:43 PM UTC 2026
% Result : Unsatisfiable 3.76s 3.25s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 14 RR)
% Number of literals : 41 ( 40 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(p12x_4,hypothesis,
inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_4) ).
cnf(p12x_2,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_2) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(p12x_1,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_1) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(prove_p12x,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p12x) ).
cnf(c_0_11,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_12,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_13,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_14,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_15,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_16,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_17,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_18,plain,
multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_19,hypothesis,
inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(X2)),
p12x_4 ).
cnf(c_0_20,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
p12x_2 ).
cnf(c_0_21,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_22,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_24,hypothesis,
multiply(inverse(least_upper_bound(X1,X2)),X1) = greatest_lower_bound(identity,multiply(inverse(X2),X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,hypothesis,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_26,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
p12x_1 ).
cnf(c_0_27,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_28,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_22]),c_0_22]) ).
cnf(c_0_29,plain,
multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_30,hypothesis,
greatest_lower_bound(identity,multiply(inverse(a),c)) = greatest_lower_bound(identity,multiply(inverse(b),c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_24]) ).
cnf(c_0_31,hypothesis,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27]) ).
cnf(c_0_32,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_12,c_0_28]) ).
cnf(c_0_33,hypothesis,
multiply(a,greatest_lower_bound(identity,multiply(inverse(b),c))) = greatest_lower_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_28]),c_0_28]),c_0_22]),c_0_27]),c_0_31]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_11,c_0_32]) ).
cnf(c_0_35,hypothesis,
greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(a),greatest_lower_bound(c,b)),
inference(spm,[status(thm)],[c_0_14,c_0_33]) ).
cnf(c_0_36,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_34]),c_0_22]) ).
cnf(c_0_37,hypothesis,
multiply(b,multiply(inverse(a),greatest_lower_bound(c,b))) = greatest_lower_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_35]),c_0_28]),c_0_28]),c_0_22]),c_0_27]) ).
cnf(c_0_38,hypothesis,
inverse(a) = inverse(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_11]),c_0_32]),c_0_22]) ).
cnf(c_0_39,negated_conjecture,
a != b,
prove_p12x ).
cnf(c_0_40,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_38]),c_0_28]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP181-3 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:27:01 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.76/3.25 % Version : CSE_E---1.7
% 3.76/3.25 % Problem : theBenchmark.p
% 3.76/3.25 % SZS status Unsatisfiable for theBenchmark.p
% 3.76/3.25 % SZS output start CNFRefutation
% See solution above
% 3.76/3.26 % Total time : 2.380s
%------------------------------------------------------------------------------