%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP395-1 : 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 : n025.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 04:26:01 PM UTC 2026
% Result : Satisfiable 1.27s 1.72s
% Output : Saturation 1.27s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
( product(X1,X4,X5,X7)
| ~ product(X1,X2,X3,X4)
| ~ product(X1,X3,X5,X6)
| ~ product(X1,X2,X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',associativity2) ).
cnf(left_inverse,axiom,
product(X1,inverse(X1,X2),X2,identity_for(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',left_inverse) ).
cnf(right_identity,axiom,
product(X1,X2,identity_for(X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',right_identity) ).
cnf(associativity1,axiom,
( product(X1,X2,X6,X7)
| ~ product(X1,X2,X3,X4)
| ~ product(X1,X3,X5,X6)
| ~ product(X1,X4,X5,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',associativity1) ).
cnf(right_inverse,axiom,
product(X1,X2,inverse(X1,X2),identity_for(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',right_inverse) ).
cnf(total_function2,axiom,
( X5 = X4
| ~ product(X1,X2,X3,X4)
| ~ product(X1,X2,X3,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',total_function2) ).
cnf(left_identity,axiom,
product(X1,identity_for(X1),X2,X2),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',left_identity) ).
cnf(total_function1_1,axiom,
( product(X2,X1,X3,multiply(X2,X1,X3))
| ~ group_member(X1,X2)
| ~ group_member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',total_function1_1) ).
cnf(identity_in_group,axiom,
group_member(identity_for(X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',identity_in_group) ).
cnf(total_function1_2,axiom,
( group_member(multiply(X2,X1,X3),X2)
| ~ group_member(X1,X2)
| ~ group_member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',total_function1_2) ).
cnf(inverse_in_group,axiom,
( group_member(inverse(X2,X1),X2)
| ~ group_member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',inverse_in_group) ).
cnf(c_0_11,axiom,
( product(X1,X4,X5,X7)
| ~ product(X1,X2,X3,X4)
| ~ product(X1,X3,X5,X6)
| ~ product(X1,X2,X6,X7) ),
associativity2,
[final] ).
cnf(c_0_12,axiom,
product(X1,inverse(X1,X2),X2,identity_for(X1)),
left_inverse,
[final] ).
cnf(c_0_13,plain,
( product(X1,X2,X3,X4)
| ~ product(X1,X5,inverse(X1,X3),X2)
| ~ product(X1,X5,identity_for(X1),X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]),
[final] ).
cnf(c_0_14,axiom,
product(X1,X2,identity_for(X1),X2),
right_identity,
[final] ).
cnf(c_0_15,axiom,
( product(X1,X2,X6,X7)
| ~ product(X1,X2,X3,X4)
| ~ product(X1,X3,X5,X6)
| ~ product(X1,X4,X5,X7) ),
associativity1,
[final] ).
cnf(c_0_16,axiom,
product(X1,X2,inverse(X1,X2),identity_for(X1)),
right_inverse,
[final] ).
cnf(c_0_17,axiom,
( X5 = X4
| ~ product(X1,X2,X3,X4)
| ~ product(X1,X2,X3,X5) ),
total_function2,
[final] ).
cnf(c_0_18,axiom,
product(X1,identity_for(X1),X2,X2),
left_identity,
[final] ).
cnf(c_0_19,plain,
( product(X1,X2,X3,X4)
| ~ product(X1,X4,inverse(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]),
[final] ).
cnf(c_0_20,axiom,
( product(X2,X1,X3,multiply(X2,X1,X3))
| ~ group_member(X1,X2)
| ~ group_member(X3,X2) ),
total_function1_1,
[final] ).
cnf(c_0_21,axiom,
group_member(identity_for(X1),X1),
identity_in_group,
[final] ).
cnf(c_0_22,plain,
( product(X1,X2,X3,identity_for(X1))
| ~ product(X1,X4,inverse(X1,X5),X3)
| ~ product(X1,X2,X4,X5) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]),
[final] ).
cnf(c_0_23,plain,
( X1 = X2
| ~ product(X3,identity_for(X3),X2,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]),
[final] ).
cnf(c_0_24,plain,
product(X1,identity_for(X1),X2,inverse(X1,inverse(X1,X2))),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_25,plain,
( product(X1,X2,X3,identity_for(X1))
| ~ product(X1,X2,X4,inverse(X1,X5))
| ~ product(X1,X4,X5,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]),
[final] ).
cnf(c_0_26,plain,
( product(X1,X2,identity_for(X1),multiply(X1,X2,identity_for(X1)))
| ~ group_member(X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]),
[final] ).
cnf(c_0_27,plain,
( product(X1,X2,X3,identity_for(X1))
| ~ product(X1,identity_for(X1),inverse(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_14]),
[final] ).
cnf(c_0_28,plain,
inverse(X1,inverse(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_24]),
[final] ).
cnf(c_0_29,plain,
( product(X1,identity_for(X1),X2,identity_for(X1))
| ~ product(X1,X3,inverse(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]),
[final] ).
cnf(c_0_30,plain,
( product(X1,X2,X3,identity_for(X1))
| ~ product(X1,X2,identity_for(X1),inverse(X1,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_18]),
[final] ).
cnf(c_0_31,plain,
( product(X1,X2,X3,X4)
| ~ product(X1,X5,identity_for(X1),X3)
| ~ product(X1,X2,X5,X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]),
[final] ).
cnf(c_0_32,plain,
( product(X1,X2,X3,X4)
| ~ product(X1,X2,X5,identity_for(X1))
| ~ product(X1,X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]),
[final] ).
cnf(c_0_33,plain,
( product(X1,X2,identity_for(X1),X3)
| ~ product(X1,X4,X5,X3)
| ~ product(X1,X4,X5,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_14]),
[final] ).
cnf(c_0_34,plain,
( product(X1,X2,inverse(X1,X3),X4)
| ~ product(X1,X5,identity_for(X1),X4)
| ~ product(X1,X5,X3,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]),
[final] ).
cnf(c_0_35,plain,
( product(X1,X2,X3,X4)
| ~ product(X1,X5,identity_for(X1),X2)
| ~ product(X1,X5,X3,X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_18]),
[final] ).
cnf(c_0_36,axiom,
( group_member(multiply(X2,X1,X3),X2)
| ~ group_member(X1,X2)
| ~ group_member(X3,X2) ),
total_function1_2,
[final] ).
cnf(c_0_37,plain,
( X1 = X2
| ~ product(X3,X2,identity_for(X3),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_14]),
[final] ).
cnf(c_0_38,plain,
product(X1,identity_for(X1),identity_for(X1),multiply(X1,identity_for(X1),identity_for(X1))),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_39,plain,
( product(X1,inverse(X1,X2),X3,identity_for(X1))
| ~ product(X1,identity_for(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]),
[final] ).
cnf(c_0_40,plain,
( product(X1,identity_for(X1),X2,identity_for(X1))
| ~ product(X1,inverse(X1,X3),X3,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]),
[final] ).
cnf(c_0_41,plain,
( product(X1,X2,inverse(X1,X3),identity_for(X1))
| ~ product(X1,X2,identity_for(X1),X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]),
[final] ).
cnf(c_0_42,plain,
( product(X1,X2,identity_for(X1),identity_for(X1))
| ~ product(X1,X2,X3,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_16]),c_0_28]),
[final] ).
cnf(c_0_43,plain,
( product(X1,inverse(X1,X2),X3,identity_for(X1))
| ~ product(X1,X2,identity_for(X1),X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_12]),
[final] ).
cnf(c_0_44,plain,
( product(X1,X2,identity_for(X1),inverse(X1,X3))
| ~ product(X1,X2,X3,identity_for(X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_16]),
[final] ).
cnf(c_0_45,plain,
( product(X1,X2,identity_for(X1),identity_for(X1))
| ~ product(X1,X3,inverse(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_16]),
[final] ).
cnf(c_0_46,plain,
( product(X1,X2,identity_for(X1),identity_for(X1))
| ~ product(X1,inverse(X1,X3),X3,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_12]),
[final] ).
cnf(c_0_47,plain,
( product(X1,X2,inverse(X1,X2),X3)
| ~ product(X1,identity_for(X1),identity_for(X1),X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_18]),
[final] ).
cnf(c_0_48,plain,
( product(X1,X2,X3,identity_for(X1))
| ~ product(X1,inverse(X1,X2),identity_for(X1),X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_16]),
[final] ).
cnf(c_0_49,plain,
( product(X1,identity_for(X1),X2,X3)
| ~ product(X1,X2,identity_for(X1),X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_16]),c_0_28]),
[final] ).
cnf(c_0_50,plain,
( product(X1,X2,identity_for(X1),X3)
| ~ product(X1,X2,inverse(X1,X3),identity_for(X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_12]),
[final] ).
cnf(c_0_51,plain,
( product(X1,identity_for(X1),X2,X3)
| ~ product(X1,X3,identity_for(X1),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_18]),
[final] ).
cnf(c_0_52,plain,
( product(X1,X2,X3,X2)
| ~ product(X1,identity_for(X1),identity_for(X1),X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_14]),
[final] ).
cnf(c_0_53,plain,
( product(X1,X2,identity_for(X1),X3)
| ~ product(X1,identity_for(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_18]),
[final] ).
cnf(c_0_54,plain,
( product(X1,X2,inverse(X1,X3),X4)
| ~ product(X1,X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_28]),
[final] ).
cnf(c_0_55,plain,
( product(X1,X2,X3,X3)
| ~ product(X1,X2,identity_for(X1),identity_for(X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_18]),
[final] ).
cnf(c_0_56,plain,
( product(X1,X2,inverse(X1,X3),identity_for(X1))
| ~ product(X1,X3,identity_for(X1),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_16]),
[final] ).
cnf(c_0_57,plain,
( product(X1,X2,X3,identity_for(X1))
| ~ product(X1,inverse(X1,X3),identity_for(X1),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_12]),
[final] ).
cnf(c_0_58,plain,
( product(X1,X2,identity_for(X1),X3)
| ~ product(X1,X3,identity_for(X1),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_14]),
[final] ).
cnf(c_0_59,plain,
( product(X1,X2,X3,X3)
| ~ product(X1,identity_for(X1),identity_for(X1),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_18]),
[final] ).
cnf(c_0_60,plain,
( group_member(multiply(X1,X2,identity_for(X1)),X1)
| ~ group_member(X2,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_21]),
[final] ).
cnf(c_0_61,plain,
( X1 = identity_for(X2)
| ~ product(X2,X3,inverse(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]),
[final] ).
cnf(c_0_62,plain,
( X1 = identity_for(X2)
| ~ product(X2,inverse(X2,X3),X3,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]),
[final] ).
cnf(c_0_63,axiom,
( group_member(inverse(X2,X1),X2)
| ~ group_member(X1,X2) ),
inverse_in_group,
[final] ).
cnf(c_0_64,plain,
multiply(X1,identity_for(X1),identity_for(X1)) = identity_for(X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]),
[final] ).
cnf(c_0_65,plain,
inverse(X1,identity_for(X1)) = identity_for(X1),
inference(spm,[status(thm)],[c_0_23,c_0_16]),
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP395-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:33:58 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Satisfiable for theBenchmark.p
% 1.27/1.72 % SZS output start Saturation
% See solution above
% 1.27/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------