%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP398-3 : TPTP v9.2.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 04:26:02 PM UTC 2026
% Result : Satisfiable 1.23s 1.71s
% Output : Saturation 1.23s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(closure_of_multiply,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| multiply(X1,X2) != X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_multiply) ).
cnf(closure_of_inverse,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_inverse) ).
cnf(c_0_5,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity,
[final] ).
cnf(c_0_6,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse,
[final] ).
cnf(c_0_7,axiom,
multiply(identity,X1) = X1,
left_identity,
[final] ).
cnf(c_0_8,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]),
[final] ).
cnf(c_0_9,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_10,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_11,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_9,c_0_10]),
[final] ).
cnf(c_0_12,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_11]),
[final] ).
cnf(c_0_13,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_14,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_6,c_0_12]),
[final] ).
cnf(c_0_15,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).
cnf(c_0_17,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_15]) ).
cnf(c_0_18,axiom,
( subgroup_member(X3)
| ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| multiply(X1,X2) != X3 ),
closure_of_multiply,
[final] ).
cnf(c_0_19,axiom,
( subgroup_member(inverse(X1))
| ~ subgroup_member(X1) ),
closure_of_inverse,
[final] ).
cnf(c_0_20,plain,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
inference(spm,[status(thm)],[c_0_16,c_0_8]),
[final] ).
cnf(c_0_21,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_12]),
[final] ).
cnf(c_0_22,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_6,c_0_17]),
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP398-3 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n031.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 18:35:38 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.23/1.71 % Version : CSE_E---1.7
% 1.23/1.71 % Problem : theBenchmark.p
% 1.23/1.71 % SZS status Satisfiable for theBenchmark.p
% 1.23/1.71 % SZS output start Saturation
% See solution above
% 1.23/1.71 % Total time : 1.369s
%------------------------------------------------------------------------------